document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=891533>Question 891533</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Solve the exponential equation using logarithms, rounding the answer to the nearest thousandth (3 decimal places). Show your work.   <BR>\n" );
document.write( "2 = 7x+3   </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #539807 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/cgi-bin/show-face.mpl?user=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=539807\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> I gather your equation is:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "2 = 7^(x+3)\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "it's hard to figure out what it is by the way that you wrote it, but I'm taking a guess that this is  the equation you wanted to show.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Assuming that it is, your solution would be as follows:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "take the log of both sides of the equation to get:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "log(2) = log(7^(x+3))\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "since log(7^(x+3)) is equivalent to (x+3)*log(7), your equation becomes:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "log(2) = (x+3) * log(7)\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "divide both sides of this equation by log(7) and you get:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "log(2) / log(7) = x + 3\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "solve for x + 3 using your calculator to get:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( ".356207... = x + 3\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "subtract 3 from both sides of this equation to get:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "x = -2.64379...\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "round this to 3 decimal places and you get:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "x = -2.644\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "That's your solution.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "replace x with the rounded value of x in the original equation and you get:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "2 = 7^(x+3) becomes 2 = 7^(-2.644 + 3) which becomes:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "2 = 7^(.356) which becomes:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "2 = 1.9991....\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "That's pretty close.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "You would be right on if you didn't round the solution.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "using the full number for x, i get:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "2 = 7^(-2.643792813 + 3) becomes:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "2 = 7^(.356207187 which becomes:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "2 = 2\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Note that .356207187 is not the full number for x + 3.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "It is the number rounded to the number of decimal places that the calculator can display.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Sometimes it's right on.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Sometimes it's not.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "I didn't use the displayed number.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "I used the internally stored number.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "That number may no even be the exact number, but, if it's not, it's at least rounded to more decimal places than the display can handle.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );